New lambert algorithm using the Hamilton-Jacobi-Bellman equation

Mai Bando, Hiroshi Yamakawa

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

A study was conducted to demonstrate the formulation of the new Lambert Algorithm using the Hamilton-Jacobi-Bellman Equation (HJB). The two-point boundary-value problem (TPBVP) of the Hamiltonian system was treated as an optimal control problem where the Lagrangian function played a role as a performance index. The approach demonstrated in the study was based on the expansion of the value function in the Chebyshev series with unknown coefficients, considering the computational advantages of the use of Chebyshev polynomials. The differential expressions that arose in the HJB equation were expanded in Chebyshev series with the unknown coefficients. The new algorithm had the potential to provide a solution to the TPVBP using the spectral information about the gravitation potential function and was applicable to the problem under a higher-order perturbed potential function without any modification.

Original languageEnglish
Pages (from-to)1000-1008
Number of pages9
JournalJournal of Guidance, Control, and Dynamics
Volume33
Issue number3
DOIs
Publication statusPublished - May 1 2010

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Chebyshev Series
Hamilton-Jacobi-Bellman Equation
Potential Function
Unknown
Differential Expression
Gravitation
Chebyshev Polynomials
Coefficient
Performance Index
Two-point Boundary Value Problem
Value Function
Hamiltonian Systems
Optimal Control Problem
optimal control
coefficients
Higher Order
boundary value problems
Hamiltonians
Formulation
polynomials

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Control and Systems Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

New lambert algorithm using the Hamilton-Jacobi-Bellman equation. / Bando, Mai; Yamakawa, Hiroshi.

In: Journal of Guidance, Control, and Dynamics, Vol. 33, No. 3, 01.05.2010, p. 1000-1008.

Research output: Contribution to journalArticle

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